We assume the photovoltaic effect will build up a space-charge field in proportion to the imprint light intensity along crystalline z-direction of [1]}, thus the \(\phi \) -dependent space-charge field on the cavity should satisfy \(E_{sc}(\phi )=E_{sc,0} \Re [\Phi _{m_0}^2(\phi )]\) . Considering the crystalline direction of x-cut LN film, the \(\phi \) -dependent refractive index modulation that inducing non-universal mode splitting can be calculated
\(\delta n(\phi ) \approx \frac{E_{sc,0}}{4n_{\rm {eff}}} \Re [ (r_{33}+r_{13}) \Phi _{m_0}^2(\phi ) + \\ \frac{(r_{33}-r_{13})}{2}(\Phi _{m_0-1}^2(\phi )+\Phi _{m_0+1}^2(\phi ))]\) 
